Preheat grill to medium-high heat.
Brush 1 tablespoon olive oil evenly over both sides of eggplant, onion, and zucchini. Sprinkle with rosemary, pepper, and salt.
Combine 1 tablespoon oil and balsamic vinegar in a bowl. Brush vinegar mixture over both sides of each slice of bread.
Place onion on grill rack coated with cooking spray, and grill for 6 minutes on each side or until tender. Remove from grill, and separate into rings.
Grill eggplant and zucchini 4 minutes on each side or until tender. Cut zucchini pieces in half crosswise.
Grill bread slices; 1-2 minutes per side or until toasted. Remove from grill.
Place half a piece of cheese on four of the bread slices; then top each serving with the following: 1 slice eggplant, 1 slice tomato, 1 basil leaf, 2 pieces zucchini, one-fourth of onion rings, 1 slice eggplant, 1 slice tomato, 1 basil leaf, 1 half piece of cheese, and top slice of bread.
Place sandwiches on grill rack; lower heat, and grill 2 minutes, covered, or until cheese melts, being care not to burn the bread.
Recipe adapted from: www.myrecipes.com